{
  "id": "math/0512094",
  "version": "v5",
  "published": "2005-12-05T14:22:48.000Z",
  "updated": "2009-05-29T09:04:07.000Z",
  "title": "The structure of the category of parabolic equations",
  "authors": [
    "Marina Prokhorova"
  ],
  "comment": "33 pages. Text improved and extended",
  "categories": [
    "math.AP",
    "math.CT"
  ],
  "abstract": "We define here the category of partial differential equations. Special cases of morphisms from an object (equation) are symmetries of the equation and reductions of the equation by a symmetry groups, but there are many other morphisms. We are mostly interested in a subcategory that arises from second order parabolic equations on arbitrary manifolds. We introduce a certain structure in this category enabling us to find the simplest representative of every quotient object of the given object, and develop a special-purpose language for description and study of structures of this kind. An example that deals with nonlinear reaction-diffusion equation is discussed in more detail.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2009-05-29T09:04:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18B99",
      "35K10",
      "35K05",
      "35K55",
      "35K57",
      "58J70"
    ],
    "keywords": [
      "second order parabolic equations",
      "partial differential equations",
      "nonlinear reaction-diffusion equation",
      "special cases",
      "special-purpose language"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12094P"
    }
  }
}